In recent years, some new generators of binary sequences, such as the clock-controlled shift register and the cascade-connected clock-controlled shift register, have been suggested. Most sequences generated by these models have period of the form (2/sup n/-1)/sup k/. Further, many other kinds of binary sequences have this kind of period. Here, the authors give the lower bound of linear complexity of all these kinds of sequences that have period of the form (2/sup n/-1)/sup k/ with n being a prime.>

It is shown that a Boolean combining function f(x) of n variables is mth-order correlation-immune if and only if its Walsh transform F( omega ) vanishes for all omega with Hamming weight between 1 and m, inclusive. This result is used to extend slightly Siegenthaler's (IEEE Trans. Comput., vol. C-34, pp. 81-85, Jan. 1985) characterization of the algebraic normal form of correlation-immune combining functions.>